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This paper addresses the cooperative promotion problem by highlighting the retailer’s private brand introduction and strategic behavior. The manufacturer engages in nationwide advertising to maintain the brand image and implements the cooperative promotion program for the retailer’s local promotional activities. The retailer can be myopic or far-sighted and is considering the introduction of a private brand. We formulate the cooperative promotion problem using the differential game approach and investigate the equilibrium control strategies under different scenarios with private brand introduction and strategic behavior. Our findings highlight that the myopic retailer is more inclined to opt for the private brand introduction compared to the far-sighted retailer. Moreover, the introduction of the retailer's private brand can also yield benefits for the manufacturer, provided that the erosive impact of the private brand is negligible. Although the retailer's myopic behavior may potentially compromise the manufacturer's brand image, it can lead to augmented profits for the manufacturer when the adverse impact of promotions remains adequately limited. Furthermore, we extend our model by incorporating the upstream competition. Our results indicate that under manufacturer competition, the retailer tends to be more cautious in opting for the private brand introduction, particularly when the erosive impact is substantial.